Why gold and platinum are precious metals?
If you observe the periodic table of elements, there are 90 elements that are found to be stable. In amongst these, other than gold (Au) and platinum (Pt) all elements have isotopes. For example if you extract iron (Fe) from an ore, it will have isotopes that have various atomic weight - 56, 57, 58, etc. Each isotope has same chemical properties but different physical properties. Gold and platinum are the only elements that have no isotopes. If you extract gold from an ore then it comes as only one isotope - with atomic weight 197. Thus, the gold will be completely pure, displaying a definite physical as well chemical property. It has no impurity from its own isotopes. The same can be said about platinum. This is the reason why gold and platinum are precious metals.
Both gold and platinum are also rare, extraction of this is very expensive. Thus, the cost of these elements in the market is therefore pretty high.